How do you connect the servo to the expansion shield?

If I buy this, do I have to buy the Intel® Edison with Arduino Breakout Kit separately?

Hello. I already own this kit and it indeed works very well when using Adruino codebase. Analog sensors are easy to use with MRAA, digital not so much..
Regarding the LCD, where can I find some proper description so can adapt this source to use it:
https://github.com/Seeed-St...

I know they are your competitors but the code they supply is very useful.

Intel Edison is compatible with Arduino, which makes it could work with these sensor directly. And the analog value sensors are easier to use than other sensor. Actually I2C sensors also could work with Edison, but you need to change its library.

I am afraid it will be a little complicated to control LCD with MRAA. Generally it is based on Arduino,

3 Pin JST connector cable, which comes with the sensor.